The Mets invited 8 non-roster players to spring training in 2020. On average, 28% of non-roster players invited to spring training play for the Mets that year. Assume that each of the 8 non-roster players has a 28% chance of playing for the Mets in 2020 and that whether any player plays for the Mets in 2020 is independent of whether any other player plays for the Mets in 2020. Let X = the number of the 8 invited non-roster players who play for the Mets in 2020. (X is a random variable) Let p = the probability of an invited non-roster player playing for the Mets in 2020.

a. What is the value of p?
b. What is the probability that X none of the invited players play for the Mets in 2020?
c. What is the probability that X = ?
d. What is the probability that X > 4?
e. What is the expected value of X?
f. What is the expected value of x? ?
g. What is the standard deviation of X?
h. What is the probability that X is within 1.4 standard deviations of its expected value?
i. What is the expected value of 3X?
j. What is the variance of 3X?